A woman arrives with her children by taxi at a public school Wednesday in New York after more than 8,000 New York City school bus drivers and aides went on strike.

NEW YORK — The first strike of New York City school bus drivers in three decades began Wednesday, leaving more than 150,000 children and their parents to negotiate new ways to class on a soggy, cold winter morning.

As anxious parents worried how long the strike would last, children boarded subways, hailed taxis and shared rides in cars while city officials warned that the labor dispute could last for some time.

“It was not easy this morning,” schools Chancellor Dennis M. Walcott said at an afternoon news conference. Still, he said, the average attendance at schools across the city was 88.5 percent, down only one percentage point from the average attendance on any given January day.

But some schools were hit harder than others, with those primarily serving special-needs children and not located near public transportation having more than a 20 percent drop in attendance in some cases.

Mayor Michael R. Bloomberg said that efforts by some strikers to disrupt alternative transportation methods were “disgraceful,” and during an afternoon news conference he offered no indication that the strike was close to an end.

“This strike is about job guarantees that the union just can’t have,” Bloomberg said.

Earlier in the day, the striking drivers’ union began running a graphic advertisement on local television channels showing the mangled wreckage of yellow school buses as a children’s chorus sings the familiar song about the wheels of the bus going round and round.

“When inexperienced drivers take your kids to school, sometimes they never get there,” a female narrator intones, before laying the blame for the strike — and any harm it causes — on Bloomberg.

While most of the city’s 1.1 million students walk or rely on public transportation to get to school, the 152,000 students who rely on school buses include 54,000 special-needs children.

“These are not kids that it is easy for them to move to mass transit,” Bloomberg said Wednesday morning during an appearance on Channel 5.

Across the city, parents hustled through the rain with children by their sides, with normal daily routines in turmoil and widespread concern about being late for their own jobs.

“I have to go to work; now I’m late,” said Catalina Torres, 51, as she dropped her three grandchildren at school. Torres, who works as a teacher’s assistant, thought about the prospect of the strike lasting more than a week (the last one, in 1979, lasted 13 weeks) and said simply, “Oh my.”

Outside schools, cars bunched up and blocked the street at times as parents, navigating the drop-off of their children at school for the first time, jockeyed for space at the curb. The police were seen at several schools helping to keep traffic moving.

Even before the union representing bus drivers, Local 1181 of the Amalgamated Transit Union, went on strike at 6 a.m., the city was making preparations to help families, including providing MetroCards and working out a system to reimburse those who used other means of transportation.

Bloomberg said the city had no plans at the moment to go to court to seek an injunction to force the drivers back to work.

The city, he said, would be holding firm. It is seeking new bids from bus companies that run some of the city’s routes, without the traditional job protection guarantees for union members that have been in past contracts. The Bloomberg administration argues that a recent court ruling has found that the city cannot offer the guarantees sought by the union.

The union has contended that the court rulings are not as clear as Bloomberg claims and has said the decision for its 8,800 drivers and matrons to strike was essentially about children’s safety. (Some buses whose drivers are members of a different union, or not unionized, are still running. The Department of Education is asking parents to call 311 or check its website for the status of particular routes.)

The Education Department said 3,000 bus routes out of approximately 7,700 total routes ran Wednesday. While only 11 percent of the routes serving general education students were running, some 38 percent of the routes for special-needs children were still in service.